Finite Group DatabasebetaFinite Group Databasebeta| order | 12654 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C19×C37 ⋊ C2×C9 |
| Hall | #20263548 ⋊ C2 |
| Hall | C37×D19 ⋊ C9 |
| Hall | D19 ⋊ #66526 |
| Sylow | C37 ⋊ AGL(1,𝔽19) |
| Sylow | C19 ⋊ C2×#66526 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C19×C37 | C2×C9 |
| LCS | G ▷ C19×C37 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,19,37|b^3=c,d^a=d^18,d^b=d^4,e^b=e^34,d^c=d^7,e^c=e^1063 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12654, 38);